20 Dissolution Technologies | NOVEMBER 2014

Formulating Buffered Dissolution Media for Sparingly Soluble Weak Acid and Weak Base Drug Compounds Based on Microenvironmental pHo Considerations

Erika S. Stippler1, Naiffer E. Romero1, and John W. Mauger2,*1U.S. Pharmacopeial Convention, 12601 Twinbrook Parkway, Rockville, MD 208522University of Utah, College of Pharmacy, Skaggs Pharmacy Institute, Department of Pharmaceutics and Pharmaceutical Chemistry, 30

South 2000 East, Salt Lake City, UT 84112

ABSTRACTThe theoretical framework for dissolution of weak acid and weak base drug compounds in buffered media is well

established. Therefore, this article is intended to provide a review of this framework and apply it to formulate buffered dissolution media based on ionic equilibrium conditions within the diffusion layer at the solidliquid interface. The pHo in the microenvironment is identified as a singularly important parameter that reflects ionic interactions between dissolving drug and buffer at the solidliquid interface. This article is focused on (1) formulating buffered dissolution media based on ionic equilibrium conditions at the solidliquid interface, (2) identifying key physicochemical parameters for both drug and buffer that are relevant to buffer formulation, and (3) providing experimental and calculation-based methods to estimate the pHo at the solidliquid interface. A shift in emphasis from relying solely on bulk buffer pH properties forms a basis for formulating buffered dissolution media and also provides insight into the physicochemical factors that affect the dissolution rate of the drug compound.

KEYWORDS: Buffered dissolution media; ionic equilibrium; pHo at solidliquid interface; self-buffering capacity; dissolution.

INTRODUCTION

The importance of buffered aqueous media to disso-lution testing is evidenced by the number of mono-graphs in the United States PharmacopeiaNational Formulary where conditions for dissolution testing are given (1). Buffer specification is typically in terms of buf-fer pH, buffer concentration, and chemical composition. These specifications focus on the bulk pH of the buffered medium and do not explicitly include the influence of the interaction between dissolving drug and buffer at the solidliquid interface in the microenvironment.

Stippler (2), Rohrs (3), and Levis et al. (4) have emphasized the importance of formulating buffered dissolution media intended for dissolution testing of sparingly soluble weak acid or weak base drug compounds. Buffered aqueous me-dium affects the dissolution rate of a sparingly soluble weak acid or weak base drug due to ionic interactions between the drug and the buffer species in the microenvironment at the solidliquid interface (514); however, the influence of the buffer can be affected by the self-buffering capacity of the dissolved drug in the microenvironment. The extent to which the buffer influences dissolution rate depends on the ionization constants of the buffer and drug, total molar concentration of the buffer and buffer capacity, concentra-tion of buffer species reacting with the drug compound, total drug solubility, and solubility of the un-ionized form of the drug compound. The pHo at the solidliquid interface

directly reflects the interaction between dissolved drug and buffer and yields data needed to estimate the relative dissolution rate of the drug. The relative dissolution rate scales the value so that the minimum is 1 under pHo condi-tions where the compound is un-ionized. Relative dissolu-tion rate values >1 reflect pHo conditions where solubility increases due to ionization of the compound.

Mass transport models applied to the dissolution of weak electrolytes in aqueous buffered media are well es-tablished. Therefore, the purpose of this article is to review and apply the principles from these models to formulate buffered dissolution media for weak acid and weak base drug compounds through an analysis of the interaction between drug and buffer at the solidliquid interface. Specifically, this article centers around (1) formulating buffered dissolution media based on ionic equilibrium conditions at the solidliquid interface, (2) identifying key physicochemical parameters for both drug and buffer that are relevant to buffer formulation, and (3) providing experimental and calculation-based methods to estimate the pHo at the solidliquid interface.

Diagrammatic Representation of the Dissolution Process and Ionic Interactions in the Microenvironment

The dissolution of a weak electrolyte drug at the solidliquid interface can be represented by the model outlined by Higuchi et al. (6). Figure 1 is a representation of steady-state dissolution for a sparingly soluble weak acid drug *Corresponding author.

e-mail: john.mauger@hsc.utah.edu

dx.doi.org/10.14227/DT210414P20

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compound in buffered dissolution medium where the drug dissolves at the solidliquid interface (x = o) and then diffuses through the aqueous diffusion layer into the bulk solution (x = h). (Throughout this article, the subscript o refers to the microenvironment at the solidliquid interface and the subscript h refers to the bulk solution.) The dissolu-tion process at the solidliquid interface will be affected by the interaction of the proton acceptor buffer species, B-, that is transported from the bulk solution into the diffusion layer where it reacts with the weak acid drug RCO2H (shown in the diagram as HA) to produce RCO2- (shown in the diagram as A-). The pHo is a reflection of the ionic equilib-rium conditions at the solidliquid interface and will affect the relative dissolution rate. A similar concentration profile can be constructed to represent the dissolution process for sparingly soluble weak base drug compounds. In the case of a weak base, the incoming reactive buffer species is a proton donor that interacts with RNH2 to form RNH3+. (A primary amine is used for illustrative purposes.)

Equilibrium Conditions at the SolidLiquid InterfaceCase I: Weak Acid Drug Compound, RCO2H

The ionic reaction that occurs between the weak acid drug compound, RCO2H, and the proton-accepting buffer species, B-, is given by

RCO2H + B- RCO2- + HB

The equilibrium expression for this ionic reaction is (6, 8)

K = Ka drug/Ka buffer = ([RCO2-][HB])/([RCO2H][B-]) (1)

The concentration of the protonated buffer species at the interface, [HB]o, is the concentration that exists in the bulk plus the amount resulting from the deprotonation of the weak acid immediately after dissolution. Therefore, [HB]o = (CHBh + [RCO2-]o). The concentration of [B-]o in the microen-vironment can be defined as [B-]o = (CB-h - [RCO2-]o). Equa-tion 1 can be rewritten using these definitions as follows:

K = ([RCO2-]o(CHBh + [RCO2-]o))/([RCO2H]o(CB-h - [RCO2-]o)) (2)

where CHBh and CB-h are the molar concentrations of the un-ionized and ionized buffer components, respectively, in the bulk buffer solution. Equation 2 can be solved for [RCO2-]o by completing the square to give

[RCO2-]o = 1/2 (- b + (b2 - 4ac)1/2) (3)

where a = 1, b = (fHBhCTotal + K[RCO2H]o), and c = - K[RCO2H]o(fB -h CTotal). The quantities fB-h and fHBh are the fractions of CB-h and CHBh, respectively, in the bulk solution, and CTotal is the total molar buffer concentration where CTotal = CB-h + CHBh.

Case II: Weak Base Drug Compound, RNH2In the case of a weak base, the ionic reaction that occurs

between the weak base drug compound, RNH2, and the proton-donating buffer species, HP, is given by

RNH2 + HP RNH3+ + P-

The equilibrium expression for this ionic interaction is given by

K = Ka buffer/Ka drug = ([RNH3+][P-]) /([RNH2][HP]) (4)

The concentration of P- in the microenvironment can be defined as [P-]o = (CP-h + [RNH3+]o), and the concentration of HP in the microenvironment can be defined as [HP]o = (CHPh [RNH3+]o). Equation 4 can be rewritten using these definitions as follows:

K = ([RNH3+]o(CP-h + [RNH3+]o))/([RNH2]o(CHPh [RNH3+]o)) (5)

where CHPh and CP_ h are the molar concentrations of the un-ionized and ionized buffer species, respectively, in the bulk buffer solution. Equation 5 can be solved for [RNH3+]o by completing the square to give

[RNH3+]o = 1/2 (- b + (b2 - 4ac)1/2) (6)

where a = 1, b = (fP-hCTotal + K[RNH2]o), and c = - K[RNH2]o (fHPh CTotal). The quantities fP-h and fHPh are the fractions of CP-h and CHPh, respectively, in the bulk solution, and CTotal is the total molar buffer concentration where CTotal = CP-h + CHPh.

Equations 3 and 6 must be considered approximate since they assume that the diffusion coefficients for all diffusing species are equal. It is advisable to carry out calculations with eqs 3 and 6 using scientific notation and a multiple digit mantissa to avoid the sensitivity of the calculation to round-off error. This analysis shows that concentrations of [RCO2-]o and [RNH3+]o will increase with

increasing values of K (i.e., Ka buffer < Ka drug for a weak acid and Ka drug < Ka buffer for a weak base);

Figure 1. Diagrammatic representation of the dissolution of a weak acid drug compound (HA), into reactive medium containing buffer species B-. Reprinted from ref 6. Copyright 1958 Wiley-Liss, Inc.

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increasing bulk concentrations of buffer species, CB-h, for a weak acid and increasing bulk concentrations of buffer species, CHPh, for a weak base; and

increasing total bulk buffer concentration, CTotal, with a corresponding increase in buffer capacity.

Therefore, buffer Ka, buffer composition, total buffer concentration, and buffer capacity can be used as param-eters to influence the concentration of ionized species of a weak acid or a weak base drug compound at the solidliquid interface. In turn, the concentration of [RCO2-]o or [RNH3+]o will influence the total solubility and relative dissolution rate.

Total Solubility and Relative Dissolution Rate for a Weak Acid and a Weak Base Drug Compound

The dissolution rate of a sparingly soluble weak electro-lyte drug is proportional to the total solubility (6, 8) where the total solubility, Stotal, for a weak acid drug compound, RCO2H, in the microenvironment is defined by

Stotal = [RCO2H]o + [RCO2-]o = [RCO2H]o(1 +Ka drug /[H+]o) (7)

where [RCO2H]o is the equilibrium solubility of the un-ionized drug at a specified temperature, [RCO2-]o is the molar concentration of the ionized species, and [H+]

o is the hydrogen ion concentration at the solidliquid interface. Equation 7 predicts that the total solubility will decrease when pHo < pKa drug and increase when pHo > pKa drug.

For a weak base drug compound, RNH2, the total solu-bility in the microenvironment is defined by

Stotal = [RNH2]o + [RNH3+]o = [RNH2]o (1 + [H+]o/Ka drug) (8)

where [RNH2]o is the equilibrium solubility of the un-ionized weak base at a specified temperature, [RNH3+]o is the molar concentration of the ionized species, and [H+]o is the hydro-gen ion concentration at the solidliquid interface. Equa-tion 8 predicts that the total solubility will decrease when pHo > pKa drug and increase when pHo < pKa drug.

The relationship between total drug solubility and the dissolution rate for the un-ionized drug species, Ru, is given by

Ru = k [RCO2H]o for a weak acid and Ru = k [RNH2]o for a weak base (9)

When pH pKa drug, then

RTotal = k ([RCO2H]o + [RCO2-]o) for a weak acid and

RTotal = k ([RNH2]o + [RNH3+]o) for a weak base (10)

From eqs 9 and 10, the relative dissolution rate, Rrel, is then defined as

Rrel = RTotal/Ru = (1 + Ka drug/[H+]o) for a weak acid and (11)

Rrel = RTotal/Ru = (1 + [H+]o/Ka drug) for a weak base (12)

Equations 912 are approximate since they assume that the diffusion coefficients for all diffusing species are equal. Equations 11 and 12 predict that the relative dissolution rate will be approximately 1 when pHo > pKa drug, in the case of a weak base. These equations also predict that the relative dissolution rate will increase when pHo > pKa drug for a weak acid and pHo < pKa drug for a weak base. As empha-sized by Ozturk et al. (9), the pHo in the microenvironment, not the bulk pHh, is the parameter that reflects the ionic interactions in the diffusion layer. Therefore, the predic-tion of the relative dissolution rate based on pHbulk may be inaccurate. This shift in emphasis from relying solely on bulk buffer properties forms a basis for formulating buffered dissolution media and provides insight into physicochemical factors that affect the relative dissolution rate of the drug compound, such as self-buffering capacity of sparingly soluble weak electrolyte drugs.

Self-Buffering Capacity of a Weak Acid or Weak Base Drug Compound in the Microenvironment

As shown in Figure 1, a saturated solution of un-ionized drug, RCO2H (shown in the diagram as HA), occurs at the solidliquid interface. The un-ionized species undergoes dissociation to yield RCO2- (shown as A-) and H+. An esti-mate of pHo for a saturated solution of a weak acid in an unbuffered aqueous medium is given by

pHo = pKa drug log [RCO2H]o (13a)

A similar situation occurs with a weak base drug com-pound where a saturated solution of un-ionized drug, RNH2, occurs at the solidliquid interface and dissociates to yield RNH3+ and OH-. An estimate of pHo for a saturated solution of a weak base drug compound in an unbuffered aqueous medium is given by

pHo = (pKw + pKa drug) + log[RNH2]o (13b)

Therefore, a weak acid or a weak base is able to contribute to its own pHo and selfbuffering capacity in the microenviron-ment. Equations 13a and 13b show that pHo is influenced by both pKa drug and the solubility of the un-ionized drug. The selfbuffering capacity increases with increasing solubility of the un-ionized species of the drug compound (10).

As a consequence of the selfbuffering capacity of the drug compound, the relationship between pHo and pHbulk is an important aspect to consider in formulating a buffered dissolution medium for a weak acid or weak base drug compound. As noted by Mooney et al. (10), pHo is expected to equal pHbulk only under conditions when the dissociation of the weak acid or weak base drug

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compound is suppressed or when the concentration of the reactive buffer species, a proton acceptor in the case of a weak acid or a proton donor in the case of a weak base, and total buffer concentration is sufficient to swamp the diffusion layer. Therefore, buffer concentration and composition are important parameters in determining the relationship between pHo and pHbulk. Since pHbulk cannot always be expected to equal pHo and since pHo directly af-fects the relative dissolution rate (9), methods to estimate pHo are needed.

Experimental and Calculation-Based Methods to Estimate [H+]o and pHoExperimental Methods

Various experimental methods are available to deter-mine pHo for weak electrolyte drugs including measuring the pH of the supernatant solution from a saturated solu-tion of drug in buffer, pH indicator dyes in conjunction with diffuse reflectance visible spectroscopy, pH sensitive spin probes to assess microenvironmental pH, confocal microscopy to image pH sensitive fluorescent dyes, and micro pH probes (15). Micro and surface pH electrodes have also been used to determine pHo for drug formula-tions, such as internally buffered drug formulations of fu-rosemide (16), controlled-release formulations of telmisar-tan (17), and tablet formulations of a poorly soluble weak base, isradipine (18).

Calculation-Based MethodsThe following relationships provide a method to estimate [H+]o and pHo.

For a weak acid:[H+]o = ([RCO2H]o Ka drug)/ [RCO2-]o where [RCO2-]o is

estimated from eq 3;

pHo = pKa drug + log ([RCO2-]o/[RCO2H]o) (14)

For a weak base:[H+]o = ([RNH3+]o Ka drug)/[RNH2]o where [RNH3+]o is esti-

mated from eq 6;

pHo = pKa drug + log([RNH2]o/[RNH3+]o) (15)

Equation 14 predicts that pHo will increase with increas-ing concentration of [RCO2-]o in the case of a weak acid, and eq 15 predicts that pHo is will decrease with increas-ing concentration of [RNH3+]o in the case of a weak base. Therefore, pHo can be influenced through the parameters that affect the production of either [RCO2-]o or [RNH3+]o, such as the total buffer concentration and the concentra-tion of buffer species CB-h in the case of a weak acid drug compound or the concentration of buffer species CHPh in the case of a weak base drug compound.

One situation where equations used to estimate pHo would not be expected to provide a quantitative relation-ship occurs when there is an interaction between drug and buffer ingredients, such as with divalent cations or surfactants. Another situation occurs for a drug formula-tion where excipients may affect ionic equilibria in the microenvironment.

Experimental and Calculation-Based Values for pHo for a Weak Acid Drug Compound, Ibuprofen, and a Weak Base Drug Compound, BupivacaineCase I: Weak Acid Drug Compound, Ibuprofen, in a Phosphate Buffer

Experimental pHo data in Table 1 were determined from the supernatant of saturated solutions of ibupro-fen (ibuprofen USP Spectrum lot 2CHO353) dissolved in USP phosphate buffer systems of known concentration.

Table 1. Experimental and Calculated Values for pHo and Relative Dissolution Rate for a Weak Acid, Ibuprofen

Total Buffer Concentration (phosphate)

Initial Buffer pH CHPO4-2 at Initial Buffer pH

CH2PO4- at Initial Buffer pH

[RCO2-]o Calculateda

Calculated pHob Experimental pHo

Calculated Relative Dissolution Ratec

0.05M 6.80 2.31E-02 2.69E-02 1.42E-02 6.20 6.13 37/1

0.025M 6.80 1.16E-02 1.34E-02 8.64E-03 5.99 5.92 23/1

0.0125M 6.80 5.78E-03 6.72E-03 4.91E-03 5.74 5.69 14/1

0.05M 7.20 3.42E-02 1.58E-02 2.17E-02 6.39 6.36 63/1

0.025M 7.20 1.71E-02 7.90E-03 1.30E-02 6.16 6.15 39/1

0.0125M 7.20 8.55E-03 3.95E-03 7.29E-03 5.91 5.91 23/1

0.05M 7.60 4.22E-02 7.80E-03 2.74E-02 6.49 6.44 75/1

0.025M 7.60 2.11E-02 3.90E-03 1.62E-02 6.26 6.27 51/1

0.0125 7.60 1.06E-02 1.90E-03 9.03E-03 6.01 6.06 32/1

a Calculated using eq 3; Ka for phosphate buffer system used to calculate pHo; pKa buffer = 6.865 (ref 19). Thermodynamic ionization constant data for several buffer systems are available in ref 20; pKa drug = 4.57; [HA]o = 3.3E-04M (4).

b Calculated using eq 14.c Calculated using eq 11 for a weak acid with experimentally determined values for [H+]o.

24 Dissolution Technologies | NOVEMBER 2014

Phosphate buffer systems were chosen since the USP specifies this buffer for dissolution testing. The satu-rated solutions were equilibrated at 37 C. The value of K for this drug/phosphate buffer system is approximately 197.

The experimental pHo values are reasonably consistent with those calculated from eq 14 over a range of total buffer concentrations and initial buffer pH values. As was noted previously, the calculated values must be con-sidered approximate. Both calculated and experimen-tal values for pHo increase with increasing total buffer concentration and increasing concentrations of proton accepting buffer species, [HPO4-2]. The calculated relative dissolution rates increase with increasing experimental values of pHo.

Case II: Weak Base Drug Compound, Bupivacaine, in a Phosphate Buffer

The experimental pHo data in Table 2 were determined from saturated solutions of bupivacaine in 0.1 M phos-phate buffers equilibrated at 37 C (14). The value for K for this drugphosphate buffer system is approximately 24. The calculated pHo values of 6.4 and 7.5 compare reasonably well with the experimental values of 6.6 and 7.6, respectively. Experimental and calculated values for pHo decrease with increasing concentrations of proton donating buffer species, [H2PO4-]. The calculated relative dissolution rates increase with decreasing experimental values of pHo.

SUMMARYThis article has focused on (1) formulating buffered

dissolution systems based on the ionic interaction between drug and buffer at the solidliquid interface, (2) identifying key physicochemical drug and buf-fer parameters relevant to buffer formulation, and (3) providing experimental and calculation-based methods to estimate pHo. An analysis of ionic equilibria in the diffusion layer predicts that the generation of ionized drug species is dependent on total buffer concentration and corresponding buffer capacity of the buffer as well as the concentration of either proton-accepting buffer species, CB- h, in the case of a weak acid drug compound,

or proton-donating buffer species, CHPh, in the case of a weak base drug compound. The pKa of the buffer is another parameter that influences the production of ionized drug species. An analysis of the self-buffering capacity of the weak electrolyte drug compound indi-cates that total buffer concentration and buffer capacity are parameters that can be used to influence the relative dissolution rate. The pHo at the solidliquid interface is identified as being singularly important in estimating the relative dissolution rate. Calculation-based methods to determine pHo are potentially useful to estimate the sen-sitivity of pHo to parameters such as total buffer concen-tration, the concentration of buffer species, and Ka buffer. Experimental values for pHo determined under condi-tions of varying total buffer concentration and varying concentrations of buffer species are useful to confirm the sensitivity of pHo to these parameters and to provide data needed to estimate values for the relative dissolu-tion rate. These data can then be used as a screening tool when developing buffered dissolution media that is related to unique physicochemical properties of the drug compound and drug formulation.

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Table 2. Experimental and Calculated Values for pHo and Relative Dissolution Rate for a Weak Base, Bupivacainea

Total Buffer Concentration (phosphate)

Initial Buffer pH CHPO4-2 at Initial Buffer pH

CH2PO4- at Initial Buffer pH

[RNH3+]o Calculatedb

Calculated pHoc ExperimentalpHod

Calculated Relative Dissolution Rated

0.1M 5 1.30E-03 9.87E-02 2.28E-02 6.4 6.6 45/1

0.1M 7.4 7.74E-02 2.26E-02 1.90E-03 7.5 7.6 5/1

a Experimental data from ref 14.b Calculated using eq 6; [RNH2]o = 3.07E-04M at 37 C estimated from data in ref 14; pKa drug = 8.24 (ref 14); pKa buffer = 6.865 (ref 20); calculated using eq 15.c Experimental pHo data from ref 14.d Calculated using eq 12 for a weak base with experimentally determined values for [H+]o from ref 14.

Dissolution Technologies | NOVEMBER 2014 25

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